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Part B How many moles of nitrogen, N , are in 72.0 g of nitrous oxide, \( \mathrm{N}_{2} \mathrm{O} \) ? Express your answer with the appropriate units. Viow Available Hint(s) Value

Ask by Rowe Ramirez. in the United States
Mar 11,2025

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Answer

There are approximately 3.27 moles of nitrogen in 72.0 grams of nitrous oxide.

Solution

1. First, calculate the molar mass of nitrous oxide, \( \mathrm{N_2O} \). The atomic mass of nitrogen is approximately \( 14.0 \, \mathrm{g/mol} \) and that of oxygen is approximately \( 16.0 \, \mathrm{g/mol} \). Thus, the molar mass is \[ M = 2(14.0) + 16.0 = 28.0 + 16.0 = 44.0 \, \mathrm{g/mol}. \] 2. Determine the number of moles of \( \mathrm{N_2O} \) in \( 72.0 \, \mathrm{g} \) using: \[ n_{\mathrm{N_2O}} = \frac{72.0 \, \mathrm{g}}{44.0 \, \mathrm{g/mol}} \approx 1.636 \, \mathrm{mol}. \] 3. Each molecule of \( \mathrm{N_2O} \) contains 2 atoms of nitrogen. Therefore, the number of moles of nitrogen atoms is: \[ n_{\mathrm{N}} = 2 \times n_{\mathrm{N_2O}} = 2 \times 1.636 \approx 3.27 \, \mathrm{mol}. \] The final answer is \( 3.27 \, \mathrm{mol\, N} \).

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To find the number of moles of nitrogen in 72.0 g of nitrous oxide (N₂O), we first need the molar mass of N₂O. The molar mass of nitrogen (N) is approximately 14.01 g/mol, and for oxygen (O), it’s about 16.00 g/mol. Thus, the molar mass of N₂O is (2 × 14.01 g/mol) + (1 × 16.00 g/mol) = 28.02 g/mol + 16.00 g/mol = 44.02 g/mol. Now, we can calculate the number of moles of N₂O in 72.0 g: \( \text{moles of N}_2\text{O} = \frac{72.0 \text{ g}}{44.02 \text{ g/mol}} \approx 1.64 \text{ mol} \). Since each molecule of N₂O contains 2 nitrogen atoms, we multiply by 2 to find the molar amount of nitrogen: \( 1.64 \text{ mol N}_2\text{O} \times 2 \approx 3.28 \text{ mol N} \). So, the number of moles of nitrogen in 72.0 g of N₂O is approximately 3.28 mol N.

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